Question

Calculate the speed of an 7.7 x 10^4 kg airliner with a kinetic energy of 1.0 × 10^9 J.
Answer in units of ms.

Answer 1

To calculate the speed of the airliner, you can use the formula for kinetic energy:

1. Given data:

- Mass of the airliner  = 7.7 x 10^4 kg

- Kinetic energy  = 1.0 x 10^9 J

2. Formula for kinetic energy:

- Kinetic energy = 0.5 x mass x speed^2

3. Rearrange the formula to solve for speed (v):

- speed (v) = square root(2 x Kinetic Energy / mass)

4. Substitute the values:

- speed (v) = square root(2 x 1.0 x 10^9 / 7.7 x 10^4)

5. Calculate the speed:

- speed (v) = square root(2 x 1.0 x 10^9 / 7.7 x 10^4) = square root(2 x 12987.01) = square root(25974.02) ≈ 161.25 m/s

Therefore, the speed of the airliner is approximately 161.25 m/s.

Answer 2

Answer:

$\sf 161.16 \, \textsf{m/s}$

Explanation:

To find the speed of the airliner, we'll use the formula for kinetic energy:

$\Large\boxed{\boxed{\sf KE = \dfrac{1}{2}mv^2}}$

where:

• KE is the kinetic energy,
• m is the mass of the airliner, and
• v is the velocity (speed) of the airliner.

Given that:

• $\sf KE = 1.0 \times 10^9 \, \textsf{J}$
• $\sf m = 7.7 \times 10^4 \, \textsf{kg}$

Substitute the value in above formula and solve for $\sf v$:

$\sf 1.0 \times 10^9 = \dfrac{1}{2} \times (7.7 \times 10^4) \times v^2$

First, let's simplify the expression:

$\sf 1.0 \times 10^9 = 3.85 \times 10^4 \times v^2$

Now, solve for $\sf v^2$:

$\sf v^2 = \dfrac{1.0 \times 10^9}{3.85 \times 10^4}$

$\sf v^2 \approx 25974.02597$

Now, take the square root of both sides to find $\sf v$:

$\sf v \approx \sqrt{25974.02597}$

$\sf v \approx 161.1645928$

$\sf v \approx 161.16 \, \textsf{m/s (in 2 d.p.)}$

So, the speed of the airliner is approximately $\sf 161.16 \, \textsf{m/s}$.